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The denominators of the semiderivative of the Bernoulli polynomials evaluated at x = 1 and normalized by sqrt(Pi).

r := n -> int(diff(bernoulli(n, t), t) / sqrt(1 - t), t = 0..1):

a := n -> denom(r(n)): seq(a(n), n = 0..9);

# Alternative:

fb := n -> sqrt(Pi)*fracdiff(bernoulli(n, x), x, 1/2):

seq(denom(simplify(subs(x=1, fb(n)))), n = 0..9);

Cf. A346709, (numerator), A346711, A346712, A346714, A346715.

allocated for Peter LuschnyThe denominators of the semiderivative of the Bernoulli polynomials evaluated at x = 1 and normalized by sqrt(Pi).

1, 1, 3, 5, 105, 63, 77, 6435, 6435, 663, 24871, 1322685, 45885, 68425, 294975, 1479, 4083810885, 46725525, 46940355, 80555475, 509285205, 471824925, 5147492805, 116197611075, 3848337675, 111954046295, 46499760153, 21364716527, 1238763451695, 149973995325

0,3

The semiderivative is the fractional derivative of order 1/2. The Davison-Essex method is used. See A346709 for formulas and references.

Cf. A346709, A346711, A346712.

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nonn,frac

Peter Luschny, Jul 31 2021

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allocated for Peter Luschny

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